Britain would continue to pay billions of pounds into the EU budget after Brexit to maintain cherished single-market access for the City of London and other sectors under plans being discussed by Theresa May’s cabinet.

The prime minister’s demand that Britain controls its borders and throws off the jurisdiction of EU judges has led many in London and Brussels to conclude that British-based banks and insurers would inevitably lose the “passporting” rights that allows them to trade freely in Europe.

But in a move likely to upset many Conservative Eurosceptics, Mrs May has not ruled out making future payments to the EU to secure privileged access to the single market. Finance is among the sectors most likely to benefit in any deal that recognised the “equivalence” of regulatory regimes.

On Friday, she assured Japanese carmaker Nissan that trading conditions for its Sunderland car plant would not change after Brexit, in the first suggestion that the government could pick favoured sectors to shield from the impact of leaving the EU.

Several senior ministers have told the Financial Times that the cabinet is considering how Britain could carry on paying billions of pounds into the EU budget. “We would have to be careful how we explained it,” said one minister. “But Theresa has been very careful not to rule it out.” Another senior Tory said: “With Theresa, you have to listen carefully to the silences.”

Theresa has been very careful not to rule it out

The Office for National Statistics said the average annual net British contribution to the EU between 2010-14 was £7.1bn, once the UK rebate and the flow of money back from Brussels to projects and institutions in the UK was taken into account.

On top of any future EU payments after Brexit, the UK will also face a divorce bill from the bloc for as much as €20bn, according to a Financial Times analysis.

To appease Tory Brexiters, ministers are looking at ways to finesse future payments. For example, Britain might make bigger-than-expected contributions to EU security programmes or use the aid budget to fund European projects.

Bankers are pushing the British government to find a way for the sector to keep as many of its passporting rights to access the EU single market as possible. They argue that falling back on schemes that have regulatory equivalence with the EU is too risky and would not prevent them from moving jobs from the UK.

Oliver Letwin, David Cameron’s former policy chief, said it was vital that Britain was able to sell retail financial services across the EU. “If we have to buy this market access by making continuing contributions to EU budgets, that may well be a price worth paying, given the number of UK jobs that are involved,” he said.

But Conor Burns, a Eurosceptic Conservative MP, said: “Leaving the EU doesn’t mean paying money into the EU.” He said that had been specifically rejected by the British people at the referendum on June 23.

Donald Tusk, European Council president, said last week that “the essence of Brexit” appeared to include no further budget contributions; he said the UK was heading for a “radical” break, with much looser economic relations in future.

But one senior EU diplomat said: “Even before the Brexit vote, the role of the City of London was precarious. They had an issue with the euro’s financial centre being outside the eurozone. Now that it is outside the EU, it is game over [for passporting].”

British ministers are considering making further EU budget contributions during any transitional period between Brexit, expected in 2019, and the conclusion of any European free-trade deal, which could take many more years to agree. The payments could extend even beyond that period.

Another senior EU diplomat said: “There will have to be a budgetary contribution through the transition.” However, the rebate secured by Margaret Thatcher in the 1980s would probably end. Ministers are considering options for Brexit and Downing Street is refusing to be drawn on its negotiating stance, calling any debate on future budget contributions “minutiae”.